Colloidal Model for the Prediction of the Extractionof Rare Earths Assisted by the Acidic Extractant

摘要

We propose the statistical thermodynamic model for the prediction of the liquid–liquid extraction efficiency in the case of rare-earth metal cations using the common bis(2-ethyl-hexyl)phosphoric acid (HDEHP) extractant. In this soft matter-based approach, the solutes are modeled as colloids. The leading terms in free-energy representation account for: the complexation, the formation of a highly curved extractant film, lateral interactions between the different extractant head groups in the film, configurational entropy of ions and water molecules, the dimerization, and the acidity of the HDEHP extractant. We provided a full framework for the multicomponent study of extraction systems. By taking into account these different contributions, we are able to establish the relation between the extraction and general complexation at any pH in the system. This further allowed us to rationalize the well-defined optimum in the extraction engineering design. Calculations show that there are multiple extraction regimes even in the case of lanthanide/acid system only. Each of these regimes is controlled bythe formation of different species in the solvent phase, ranging frommultiple metal cation-filled aggregates (at the low acid concentrationsin the aqueous phase), to the pure acid-filled aggregates (at thehigh acid concentrations in the aqueous phase). These results arecontrary to a long-standing opinion that liquid–liquid extractioncan be modeled with only a few species. Therefore, a traditional multipleequilibria approach is abandoned in favor of polydisperse sphericalaggregate formations, which are in dynamic equilibrium.